From c7676f10121a20ff488a5ba195b4610a9a36b1d2 Mon Sep 17 00:00:00 2001
From: dellaert <dellaert@cc.gatech.edu>
Date: Wed, 3 Dec 2014 16:41:11 +0100
Subject: [PATCH] More changes

---
 GTSAM-Concepts.md | 52 +++++++++++++++++++++++++++++++++++++----------
 1 file changed, 41 insertions(+), 11 deletions(-)

diff --git a/GTSAM-Concepts.md b/GTSAM-Concepts.md
index 6c09cc467..9b848bf51 100644
--- a/GTSAM-Concepts.md
+++ b/GTSAM-Concepts.md
@@ -10,6 +10,9 @@ Concepts define (see [Generic Programming Techniques](http://www.boost.org/commu
 
 GTSAM Types start with Uppercase, e.g., `gtsam::Point2`, and are models of the concepts MANIFOLD, GROUP, LIE_GROUP, VECTOR_SPACE
 
+traits
+------
+
 `gtsam::traits` is our way to associate these concepts with types. We will not use Eigen-style or STL-style traits, that define many properties at once. Rather, we use boost::mpl style meta-programming functions to facilitate meta-programming.
 
 Traits allow us to play with types that are outside GTSAM control, e.g., `Eigen::VectorXd`.
@@ -31,42 +34,69 @@ The naming conventions are as follows:
         typedef const int value_type; // const ?
       }
     
-* Functors: `gtsam::traits::someFunctor<T>`, i.e., they are mixedCase starting with a lowercase letter and define a functor type
+* Functors: `gtsam::traits::someFunctor<T>::type`, i.e., they are mixedCase starting with a lowercase letter and define a functor `type`. Example
     
-      template<>
-      gtsam::traits::retract<Point2> {
-        Point2 operator()(const Point2& p, const Vector2& v) {
-        	return Point2(p.x()+v[0], p.y()+v[1]);
+      struct Point2::retract {
+        Point2 p_;
+        retract(const Point2& p) : p_(p) {}
+        Point2 operator()(const Vector2& v) {
+          return Point2(p.x()+v[0], p.y()+v[1]);
         }
       }
     
-  The above is still up in the air, can we not point to a function somewhere? Or a method?
+      template<>
+      gtsam::traits::retract<Point2> {
+        typedef Point2::retract type;
+      }
+    
+  The above is still up in the air. Do we need the type indirection?
+  
+tags
+----
   
 Concepts are associated with a tag.
 
+* `gtsam::tags::manifold_tag`
+* `gtsam::tags::group_tag`
+* `gtsam::tags::lie_group_tag`
+* `gtsam::tags::vector_space_tag`
+
+Can be queried `gtsam::traits::structure_tag<T>`
+
+
 Manifold
 --------
 
-`gtsam::tags::manifold_tag`
+* types: `DefaultChart`
+* values: `dimension`
 
-`gtsam::traits::structure_tag<T>`
-
-* associated types: DefaultChart
-* valid expressions: dimension
+Anything else?
 
 Chart
 -----
 
+* types: `Manifold`, `Vector`
+* values: `retract`, `local`
+
+Are these values? They are just methods. Anything else?
+
 
 Group
 -----
 
+* values: `identity`
+* values: `compose`, `inverse`, (`between`)
+
 Lie Group
 ---------
 
+Implements both MANIFOLD and GROUP
+
 Vector Space
 ------------
 
+Lie Group where compose == `+`
+
 Examples
 --------